Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271718 | C2 | semidirect |
| 3. #14271466 | C2 | semidirect |
| 4. #14271465 | C2 | semidirect |
| 5. #14271454 | C2 | semidirect |
| 6. #14271453 | C2 | semidirect |
| 7. #14271440 | C2 | semidirect |
| 8. #14271204 | C2 | semidirect |
| 9. #14271185 | C2 | semidirect |
| 11. C29×#474 | C2 | semidirect |
| 14. C29×C4⋊Q8 | C22 | semidirect |
| 25. #11745252 | C22 | semidirect |
| 31. #11745231 | C22 | semidirect |
| 32. C29×#107 | C22 | semidirect |
| 33. C29×C4⋊C8 | C22 | semidirect |
| 37. #11745165 | C22 | semidirect |
| 38. #11745162 | C22 | semidirect |
| 40. #11745156 | C22 | semidirect |
| 41. #11745155 | C22 | semidirect |
| 42. C4⋊#6597 | C22 | semidirect |
| 50. D4×D29 | Q8 | semidirect |
| 146. #474 | D29 | semidirect |
| 160. C4⋊Q8 | C2×D29 | semidirect |
| 177. #107 | C2×D29 | semidirect |
| 182. C4⋊C8 | C2×D29 | semidirect |
| 187. C29 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271718 | 2 |
| C4×D4×D29 | 2 |
| #14271466 | 2 |
| #14271465 | 2 |
| #14271454 | 2 |
| #14271453 | 2 |
| #14271440 | 2 |
| #14271204 | 2 |
| #14271185 | 2 |
| #14271166 | 2 |
| C29×#474 | 2 |
| #3077 | 29 |